%I
%S 19,13,37,23,73,19,23,23,13,59,19,13,13,5,31,7,43,3,53,11,67,131,19,
%T 31,181,11,223,83,317,89,163,569,821,1553,109,191,109,409,709,409,509,
%U 1627,509,23,127,659,809,29,499,191,719,1409,773,967,67,139,23,229,23,11,263,11,19,293,19,331,643,331,29,59,419,13,491,71,23,13,107,13,19,139,19,59,31,109,199,113,421,733,181,89,59,47,13,17,11,41,23,5,23,17,5,5,3,13,7,23,43,73,139,17,229,11,257,71,113,7,191,311,509,337
%N a(1)=19, a(2)=13, a(3)=37; thereafter a(n) = gpf(a(n1)+a(n2)+a(n3)), where gpf = "greatest prime factor".
%C This is the periodic part of A177904  it is periodic with period 212.
%C A smaller start is a(1)=3, a(2)=13, a(3)=7, but that would not produce the terms in the order of their first appearance in A177904.
%C There are several open questions concerning this class of sequences  see the BackCaragiu reference in A177904.
%H N. J. A. Sloane, <a href="/A177923/b177923.txt">Table of n, a(n) for n = 1..212</a>
%t nxt[{a_,b_,c_}]:={b,c,FactorInteger[a+b+c][[1,1]]}; NestList[nxt,{19,13,37},120][[All,1]] (* _Harvey P. Dale_, Dec 11 2018 *)
%Y Cf. A006530, A177904, A175723.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Dec 18 2010
